"Woohoo!" That's an expression you might shout in exultation or extreme happiness. On New Year's Eve, Times Square is bursting with exultation as people shout and sing joyfully to ring in the new year.
Exultation comes from the Latin exsilire, which means "leap out or up." Think of leaping for joy and you've pretty much captured the sentiment of exultation. This word is used to describe a kind of triumphant joy, the kind you might see at the end of a football game when the winning team is pumping their fists, cheering and dumping Gatorade all over their coach.